The Fifth Card Magic Trick Puzzle

Mind Teasers :
The Fifth Card Magic Trick Puzzle

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Famous magicians Dylan Rhodes and Daniel Atlas performed an exhilarating magic trick in my last birthday party. Since, it was my birthday, Rhodes asked me to shuffle a new deck and pick any five cards out of it. I took out the cards as asked, looked at them and then showed all five cards to Rhodes. Rhodes then gave four cards to Daniel and the remaining fifth card to me. Daniel looked at the four cards for about ten seconds and then he told me what card I was holding.

Surprise, Surprise! He was right!

It was quite surprising to me at that time, but when I reached back home, I was able to crack the trick behind the magic.

The five cards must contain at least one card of the same suit.
Let's assume Rhodes placed one of the two cards of the same suit at the end and the second card was given to Daniel.
In that case, Daniel will know the suit of the card.

Now the real question is how Rhodes made sure that Daniel also knows the number of the card.

Daniel got four cards and one of them will determine the suit, so we are left with 3 cards.
3 cards can be arranged in 3! ways i.e. 6 ways but our card numbers can vary from 1 to 13.
Since we have two cards of the same suit we will make sure that we don't pick the King (13). This leaves us with 12 numbers.

We can also distinguish card from upside down position, therefore, we now have 6 * 2 ways to arrange these card.
"TADA.... We cracked the magic trick".

Let us assume that the smallest card is C1U (upwards position) and C1D (downwards position). Similarly, we have C2U, C2D, C3U and C3D

In a closed jar, there are three strawberry candies, two mango candies and five pineapple candies. You can't see inside the jar. Now, how many toffees you must take out from the jar to make sure that you have one of each flavor?

Explanation:
2 < 3 < 5
To find out the required number of candies, take one in place of the least number (i.e. take one mango candy) and then add all the greater numbers (i.e. three strawberry and five pineapple candies) to it.

This is a classic chess puzzle and considered to be one of the hardest puzzles in history.
As shown in the picture below, White army is arranged in a classic chess board. You need to add black army i.e
1 king
1 queen
2 rooks
2 bishops
2 knights
8 pawns
in such a way that not a single piece of either color is under attack.

Aishwarya Rai walks into a bank to cash out her check.
By mistake the bank teller gives her dollar amount in change, and her cent amount in dollars.
On the way home she spends 5 cent, and then suddenly she notices that she has twice the amount of her check.

A guy claims to do the following thing. He puts a coin in a glass bottle. Then, he shuts the mouth of the bottle with the help of a cork. Now he manages to remove the coin out from the bottle without taking out the cork or breaking the glass bottle.

Two trains under a controlled experiment begin at a speed of 100 mph in the opposite direction in a tunnel. A supersonic bee is left in the tunnel which can fly at a speed of 1000 mph. The tunnel is 200 miles long. When the trains start running on a constant speed of 100 mph, the supersonic bee starts flying from one train towards the other. As soon as the bee reaches the second train, it starts flying back towards the first train.

If the bee keeps flying to and fro in the tunnel till the trains collide, how much distance will it have covered in total?

A typical way will be to start thinking about summing up the distance that the bee will travel but that will be quite a tedious task. How about we offer you a much easy solution?

The tunnel is 200 miles long and the trains are running at as peed of 100 mph which means that they will collide exactly at the center of the tunnel and seeking their speed, they will collide after an hour.

Now consider the bee which is flying at a speed of 1000 mph and will keep flying till the train collides. As calculated, it will keep flying for an hour which means the distance that it will cover is 1000 miles.